Please help! Radicals.
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Answer:

Here's the answers

Step-by-step explanation:

1. When two variables are in relation with a formula or a variable is related by the sum of two or more variables, then it is a partial variation. X = KY + C (where K and C are constants) is a straight line equation which is an example of partial variation.

2. The formula y=kxn y = k x n is used for direct variation. The value k is a nonzero constant greater than zero and is called the constant of variation.

(a) The value of α, the probability of Type I error, is approximately 0.007 or 0.7%. (b) The power of the test, the probability of correctly rejecting H0, is approximately 0.0894 or 8.94% for a true mean output voltage of 5.1 volts.

To find the exact values of α and the power of the test, we need to calculate the probabilities associated with the standard normal distribution using the given Z-values.

(a) Calculating α:

Z1 = (4.85 - 5) / (0.25 / √18) ≈ -2.683

Z2 = (5.15 - 5) / (0.25 / √18) ≈ 2.683

Using a standard normal distribution table or calculator, we can find the probabilities

P(Z < -2.683) + P(Z > 2.683) ≈ 2 * P(Z > 2.683)

By looking up the value of 2.683 in the standard normal distribution table or using a calculator, we find that P(Z > 2.683) is approximately 0.0035.

Therefore, α ≈ 2 * 0.0035 = 0.007

(b) Calculating the power of the test

Z1 = (4.85 - 5.1) / (0.25 / √18) ≈ -1.699

Z2 = (5.15 - 5.1) / (0.25 / √18) ≈ 1.699

Using a standard normal distribution table or calculator, we can find the probabilities

P(Z < -1.699) + P(Z > 1.699) ≈ 2 * P(Z > 1.699)

By looking up the value of 1.699 in the standard normal distribution table or using a calculator, we find that P(Z > 1.699) is approximately 0.0447.

Therefore, the power of the test ≈ 2 * 0.0447 = 0.0894 or 8.94% (rounded to three decimal places).

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The tank with the smallest surface area has dimensions of 6ft.

s = 12ft and h = 6ft.

A(s) = s² + 4 × (V ÷ s)

The rectangular tank has a capacity of 864 feet.

Let the square base's long sides be.

Let h represent the tank's height.

Let A represent the tank's whole area.

A = (Base Area) + (4 × Lateral Area)

Lateral Area = s × h

Lateral Area = s × (V ÷ s²)

Lateral Area = (V ÷ s)

Base Area = s²

Compared to the objective function,

A(s) = s² + 4 × (V ÷ s)

A(s) = s² + 4 × (864 ÷ s)

The area function's derivative,

A'(s) = 2s - (3456 ÷ s²)

The smallest surface area is now.

A'(s) = 0

2s - (3456 ÷ s²) = 0

2 × \(s^{3}\) = 3456

\(s^{3}\) = 3456

s = \(\sqrt[3]{3456}\)

s = 12ft

The volume is,

V = s² × h

864 = 12² × h

h = 6ft

As a result, the tank's height is 6 feet, and the square base's long sides measure 12 feet.

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The question is -

A rectangular tank with a square​ base, an open​ top, and a volume of 864 ft cubed is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area. Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.

The probability P(X=2, Y+Z ≤ 3) is 13. Random variables are variables in probability theory that represent the outcomes of a random experiment or event.

To find the probability P(X=2, Y+Z ≤ 3), we need to sum up the joint probabilities of all possible combinations of X=2, Y, and Z that satisfy the condition Y+Z ≤ 3.

Step 1: List all the possible combinations of X=2, Y, and Z that satisfy Y+Z ≤ 3:

X=2, Y=1, Z=1

X=2, Y=1, Z=2

X=2, Y=2, Z=1

Step 2: Calculate the joint probability for each combination:

For X=2, Y=1, Z=1:

f(2, 1, 1) = (2+1) * 1 = 3

For X=2, Y=1, Z=2:

f(2, 1, 2) = (2+1) * 2 = 6

For X=2, Y=2, Z=1:

f(2, 2, 1) = (2+2) * 1 = 4

Step 3: Sum up the joint probabilities:

P(X=2, Y+Z ≤ 3) = f(2, 1, 1) + f(2, 1, 2) + f(2, 2, 1) = 3 + 6 + 4 = 13

They assign numerical values to the possible outcomes of an experiment, allowing us to analyze and quantify the probabilities associated with different outcomes.

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The number of plants Ethan has are 5.

Two or more expressions with an Equal sign is called as Equation.

Let x be the number of plants Ethan has.

Ethan uses 3.5 ounces of water for each plant, so he will use a total of 3.5p ounces of water.

If he starts with 32 ounces of water and ends up with 14.5 ounces

Total of 32 - 14.5 = 17.5 ounces of water.

As given the amount of water used is equal to the amount of water per plant times the number of plants:

3.5x = 17.5

Divide both sides by 3.5

x=5

Hence, , Ethan has 5 plants.

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Answer:

3.16666667 tons

Step-by-step explanation:

hope this helps have a good evening

Answer:

After investing for 3 years at 7% interest, your $600 investment will have grown to $735.03

Step-by-step explanation:

Answer:

288

Step-by-step explanation:

C/48 to the 15th power.

The value of `P` is returned as output by the function.

The given function is used to compute the value v defined as\(`P=∑aᵢbⱼ`.\)

Here is the implementation of the MATLAB function that takes two vectors a and b and returns the value of v as output:

MATLAB function implementation:

```function v = myValue(a, b)    % Check if both the vectors have same length    if(length(a) ~= length(b))        fprintf('Error: Vectors a and b should have same length.\n');        v = NaN;        return;    end    % Initialize the value of P to zero    P = 0;    %

Calculate the value of P    for i = 1:length(a)        P = P + a(i)*b(i);    end    % Return the value of P    v = P;end```

The function first checks if the length of the input vectors `a` and `b` is equal or not. If the length of the two vectors is not equal, an error message is displayed on the console, and the function returns `NaN`.

If the length of the vectors is the same, then the value of `P` is initialized to zero, and it is computed as the sum of the element-wise product of the vectors `a` and `b`.

Finally, the value of `P` is returned as output by the function.

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As a result, if the two angles' measurements are (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

An angle is a geometric figure formed by two rays that have a common endpoint, called the vertex. The rays are also known as the sides or legs of the angle. Angles are typically measured in degrees, with a full circle measuring 360 degrees. Angles can also be measured in radians, which are another unit of angular measurement used in mathematics and physics. One radian is equal to the angle subtended by an arc of a circle that has a length equal to the radius of the circle. The size of an angle is determined by the amount of rotation that occurs between the two rays. This is typically measured relative to the positive x-axis, with counterclockwise rotations being considered positive and clockwise rotations being considered negative. Angles are used in a wide range of mathematical and scientific applications, including geometry, trigonometry, physics, engineering, and architecture. They are also used in many everyday situations, such as measuring the size of an opening or the angle of incidence of sunlight on a surface.

Here,

If the two angles are congruent, then they must have the same measure.

So we can set the expressions for the measures of the two angles equal to each other and solve for y:

3y + 11 = 11y + 15

Subtracting 3y from both sides:

11 = 8y + 15

Subtracting 15 from both sides:

-4 = 8y

Dividing both sides by 8:

y = -1/2

Therefore, if the measure of the two angles is (3y+11) and (11y+15) and they are congruent, then y must equal -1/2.

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Answer:

5

Step-by-step explanation:

range is biggest number minus smallest number.

First arrange the numbers from least to greatest.

4, 4, 5, 6, 8, 9, 9

Subtract the biggest number, 9, from the smallest number, 4.

9 - 4 = 5

Answer:

5

Step-by-step explanation:

The range is the highest value number minus the lowest value number. 9 minus 4 is 5.

If a set contains ‘n’ elements, then the number of proper subsets of the set is 2^n - 1.

In this problem,

n = 4

2^4 - 1 = 16 - 1 = 15 proper subsets

The empirical rule may be used to determine the percentage of data values that must be within only one, two, and three standard deviations of the mean for data having a bell-shaped distribution.

The 68 95 99 rule, commonly referred to as the empirical rule in statistics, asserts that given normal distributions, 68% of observed data points will fall within one standard deviation from the mean, 95% will fall between two standard deviations, and 99.7% will happen within three standard deviations.

Fairly anticipate that your data will resemble a normal distribution, the empirical rule, the mean, as well as the standard deviation become even more beneficial. Determine probabilities and percentages for many events just by knowing these two statistics.

The term "empirical rule" derives from empirical research, which relies on measurements and observations of actual results rather than theory. In other words, the term "empirical" denotes a foundation in actuality.

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Answer:

Step-by-step explanation:

x=120°

if you look, the arrows on the lines mean they’re parallel.

so

Approximately, the LA Dodgers hit 35 home runs.

Approximation is  a mathematical quantity that is close in value to but not the same as a desired quantity

From the question

The total number of home run in the Major League Baseball is 583

The LA Dodgers home run can be gotten by finding 6% of the the total home runs

That is, 6% of 583

= \(\frac{6}{100} *\frac{583}{1}\)

= 34.98 home runs

We can conclude that LA Dodgers hit approximately 35 home runs

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Answer:

stratus

Step-by-step explanation:

cause they are dark clouds

Answer:

43.48

Step-by-step explanation:

The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer:

  PEMDAS or BIDMAS

Step-by-step explanation:

You want to know how to remember the order of operations.

Commonly used acronyms for the Order of Operations are ...

  PEMDAS

  BIDMAS

The letters of these stand for ...

  P, B — parentheses or brackets

  E, I — exponents or indices

  M, D — multiplication and division

  A, S — addition and subtraction

Expressions enclosed in grouping symbols (parentheses or brackets) have the highest precedence. They are evaluated first, according to the order of operations.

Exponents (indices) are evaluated next. A sequence of exponent operations, such as a^b^c is evaluated right to left, as a^(b^c), unless parentheses modify the order.

Because exponents and indices have a higher precedence than other arithmetic operations, something like 2^3x is evaluated as (2^3)x, not 2^(3x), and √2p is (√2)p, not √(2p). It is fairly common to see a square root erroneously written as 3^1/2 = (3^1)/2 = 3/2 when 3^(1/2) = √3 is intended.

Multiplication and division have the same precedence. Even though M precedes D (or D precedes M, depending on which acronym you use), they are evaluated in order of appearance left to right. As with exponents, a common error is forgetting to put parentheses around numerators and denominators. For example, 3/2π is different from 3/(2π).

Similarly, addition and subtraction have the same precedence and are evaluated in order of appearance, left to right.

The composition (ring) operator (∘) is used to signify a sequence of functional or transformation operations. For example (f∘g)(x) is the composition of functions f and g. The functions or transformations in a composition are evaluated right to left:

  (f∘g)(x) = f(g(x))

Operations performed on functions can be written in confusing ways. For example, ...

  \(y = f^{-1}(x)\qquad\text{means }x=f(y),\text{ not }y=\dfrac{1}{f(x)}\)

The notation using a positive exponent stands in contrast:

  \(\sin^4(x)\qquad\text{usually means }(\sin(x))^4,\text{ not }\sin(\sin(\sin(\sin(x))))\)

On the other hand, an exponent applied to a function name can mean recursive application of the function, as in sin²( ) = sin(sin(...)). It can also mean an n-th derivative. Context is important in such situations.

Answer: x = 3

Step-by-step explanation:

Let's solve your equation step-by-step.

31 = 8x + 7

Step 1: Flip the equation.

8x + 7 = 31

Step 2: Subtract 7 from both sides.

8x + 7 − 7 = 31 − 7

8x = 24

Step 3: Divide both sides by 8.

8x /8  =  24 /8

x = 3

Answer:

x = 3

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Have a great day!!

Answer:

0.0072

Step-by-step explanation:

=7.2 × 10^-3

=7.2 × 10/10000

=7.2 ×1/1000

=0.0072

Answer:

0.00072

Step-by-step explanation:

Step 1: We know that we will have 3 zeros because of the exponent, and the exponent happens to be negative, so we will have the 3 zeros in after the decimal point (obviously), but before any numbers.

Step 2: We will then convert the 7.2 into 72, and it will also go after the decimal point. It will also go after the 3 zeros.

Step 3: Put it all together. The 0 (0), the decimal point (0.), the three zeros (0.000), and the 72 (0.00072). 0.00072 is your answer!

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3 = 2 by z property

Step-by-step explanation:

Congruence criteria for triangles

If two sides and the angle between them in one triangle have the same measures as two sides and the angle between them in another triangle, then the triangles are congruent.

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Answer:

Step-by-step explanation:

Dont do it. Just take the detention

Answer:

2°C

Step-by-step explanation:

5 × ( - 2 ) - 4 × ( - 3 ) = - 10 + 12 = 2

The temperature on the 5th day is 2°C .

A) The expression represent the area of the rectangle is \(x^2+30x-1000\) \(ft^2\)

B) For 50 ft, Area = 3000 \(\rm ft^2\), For 100 ft , area = \(\rm 12000\ ft^2\) and For 150 ft, area = 26000 \(\rm ft^2\)

C)  If area of the square is larger than new rectangle play ground then we need enough time to play.

The area of a rectangle οccupies is the space it takes up inside the limitatiοns οf its fοur sides. The dimensiοns οf a rectangle determine its area. In essence, the area οf a rectangle is equal tο the sum οf its length and breadth.

Let us take side length οf the square = x

Adding 50 feet fοr οne side then , length οf rectangle = x+50 feet.

Nοw decreasing 20 feet fοr οther side then, width οf rectangle = x- 20 feet.

A) Now area of the rectangle is ,

A = length*width

=> A = (x+50)(x-20)

=> A = \(x^2-20x+50x-1000\)

=> A = \(x^2+30x-1000\)

Then , the expression represent the area of the rectangle is \(x^2+30x-1000\) \(ft^2\)

B) If side length x= 50 ft then

Area = \(50^2+30\times50-1000 = 2500+1500-1000 = 3000 ft^2\)

If side length x = 100 ft then

Area = \(100^2+30\times100-1000 = 10000+3000-1000 = 12000 ft^2\)

If side length = 150 ft then

Area = \(150^2+30\times150-1000= 22500+4500-1000= 26000 ft^2\).

C) If area of the square is larger than new rectangle play ground then we need enough time to play.

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Each terminology should be matched to its definition as follows:

ICS is an abbreviation for incident command system and it can be defined as a subset of the National Incident Management System (NIMS) which is typically used for planned events, as well as for emergencies and coordinated responses in various business organizations and/or circumstances.

Generally speaking, there are six (6) fundamental functional areas in an incident command system (ICS) and these including the following;

In conclusion, chain of command, unity of command, and unified of command are all terminologies that are associated with an incident command system (ICS).

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Chelsea has 15 dimes and 20 nickels in her pocket. She has a total of $2.50 in dimes and nickels. The number of nickels is five more than the number of dimes.

1. Let's assume that Chelsea has x dimes. According to the problem, she has five more nickels than dimes, which means she has x + 5 nickels. The value of x dimes is $0.10x, as each dime is worth $0.10. The value of (x + 5) nickels is $0.05(x + 5), as each nickel is worth $0.05.

Since the total value of the coins is $2.50, we can set up the equation:

$0.10x + $0.05(x + 5) = $2.50

2. Simplifying the equation, we get:

$0.10x + $0.05x + $0.25 = $2.50

$0.15x + $0.25 = $2.50

$0.15x = $2.50 - $0.25

$0.15x = $2.25

3. Dividing both sides by $0.15, we find:

x = 15

Therefore, Chelsea has 15 dimes and 15 + 5 = 20 nickels in her pocket.

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